In order to search for hydrocarbon accumulations in the earth, geoscientists are using methods of remote sensing to look below the earth's surface. A routinely used technique is the seismic reflection method where man-made sound waves are generated near the surface. The sound propagates into the earth, and whenever the sound passes from one rock layer into another, a small portion of the sound is reflected back to the surface where it is recorded. Typically, hundreds to thousands recording instruments are employed. Sound waves are sequentially excited at many different locations. From all these recordings, a two- or three-dimensional image of the subsurface can be obtained after significant data processing. Measurements derived from these data are called seismic attributes.
The most commonly used attribute is amplitude of the recorded sound waves because it allows identification and interpretation of many subsurface features such as the boundaries between different rock layers. Many other properties of the subsurface, however, are not sufficiently identifiable on images of basic seismic amplitude. The published literature describes numerous manipulations of seismic data, and thus, numerous attributes that each highlight some specific feature, relationship, or pattern that might otherwise be difficult to detect.
Taner et al. developed complex trace analysis of seismic data and defined two seismic attributes, instantaneous phase and frequency. (“Complex seismic trace analysis,” Geophysics 44, 1041-1063 (1979)) In U.S. Pat. No. 6,487,502, Taner presented a method based on instantaneous phase and frequency to estimate the shaliness of the subsurface.
In U.S. Pat. No. 5,724,309, Higgs and Luo presented a method for utilizing instantaneous phase and its derivatives as display and/or plot attributes for seismic reflection data processing and interpretation for two-dimensional and three-dimensional seismic data. Specifically, they compute the spatial frequency, dip magnitude and dip azimuth attributes of the seismic events using the rate of change of instantaneous phase with space, instantaneous frequency and seismic velocity. The results are displayed or plotted to assist interpreters in identifying fault breaks and stratigraphic features in the earth's subsurface. See also Luo et al., “Edge detection and stratigraphic analysis using 3-D seismic data,” 66th Annual International Meeting, Society of Exploration Geophysicists, 324-327 (1996).
In Two-dimensional Phase Unwrapping, Wiley-Interscience, pages 31-50 (1998), Ghiglia and Pritt present a two-dimensional method for the computation of phase residues in the context of phase unwrapping. When unwrapping the phase along a closed path, the final value equals the initial one unless the path encloses a phase residue. Making this path infinitesimal allows location and definition of discrete points termed phase residues where such inconsistencies arise. Due to the two-dimensionality, however, most residues are isolated and thus, do not line up in a systematic manner.
Huntley presents a three-dimensional extension of the phase residues in “Three-dimensional noise-immune phase unwrapping algorithm,” Applied Optics 40, 3901-3908 (2001). He demonstrates that in three dimensions, phase residues line up systematically in the shape of closed loops or open strings. He uses these loops to construct simple surfaces that disambiguate the inconsistencies arising in phase unwrapping. He then uses the resulting three-dimensional phase unwrapping algorithm as the basis for a method and apparatus for measuring the shape of objects from the projected fringes generated by optical interferometry. Huntley discloses the generation of phase residues and their conversion to simple surfaces (by interpolation) for the purpose of phase unwrapping. No further meaning or usage for phase residues is disclosed.
U.S. Pat. No. 6,850,845 to Stark presents a method to convert instantaneous phase into a monotonically increasing unwrapped phase and uses these values to ease seismic interpretation by removing structural complexity.
U.S. Pat. No. 6,278,949 to Alam presents a method for visualization of a seismic data volume that automatically highlights geologic structure and compartments without requiring manual picking.
U.S. Pat. No. 6,775,620 to Baker and U.S. Pat. No. 7,024,021 to Dunn and Czernuszenko present other methods to locate a surface in a three dimensional volume of seismic data based on automatic generation of horizons from interactively selected points.